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Efficient estimation and computation for the generalised additive models with unknown link function

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  • Lin, Huazhen
  • Pan, Lixian
  • Lv, Shaogao
  • Zhang, Wenyang

Abstract

The generalised additive models (GAM) are widely used in data analysis. In the application of the GAM, the link function involved is usually assumed to be a commonly used one without justification. Motivated by a real data example with binary response where the commonly used link function does not work, we propose a generalised additive models with unknown link function (GAMUL) for various types of data, including binary, continuous and ordinal. The proposed estimators are proved to be consistent and asymptotically normal. Semiparametric efficiency of the estimators is demonstrated in terms of their linear functionals. In addition, an iterative algorithm, where all estimators can be expressed explicitly as a linear function of Y, is proposed to overcome the computational hurdle for the GAM type model. Extensive simulation studies conducted in this paper show the proposed estimation procedure works very well. The proposed GAMUL are finally used to analyze a real dataset about loan repayment in China, which leads to some interesting findings.

Suggested Citation

  • Lin, Huazhen & Pan, Lixian & Lv, Shaogao & Zhang, Wenyang, 2018. "Efficient estimation and computation for the generalised additive models with unknown link function," Journal of Econometrics, Elsevier, vol. 202(2), pages 230-244.
    • Handle: RePEc:eee:econom:v:202:y:2018:i:2:p:230-244
    DOI: 10.1016/j.jeconom.2017.11.001
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    References listed on IDEAS

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    1. Linton, Oliver B., 2000. "Efficient Estimation Of Generalized Additive Nonparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 16(4), pages 502-523, August.
    2. Chen, Kani & Guo, Shaojun & Sun, Liuquan & Wang, Jane-Ling, 2010. "Global Partial Likelihood for Nonparametric Proportional Hazards Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 750-760.
    3. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    4. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    5. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
    6. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    7. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    8. Opsomer, Jan & Ruppert, David, 1997. "Fitting a Bivariate Additive Model by Local Polynomial Regression," Staff General Research Papers Archive 1071, Iowa State University, Department of Economics.
    9. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61, February.
    10. Scallan, A. & Gilchrist, R. & Green, M., 1984. "Fitting parametric link functions in generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 2(1), pages 37-49, June.
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